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Abstract

Delivering femtosecond laser light in the focal plane of a high numerical aperture microscope objective is still a challenge, despite significant developments in the generation of ultrashort pulses. One of the most popular techniques, used to correct phase distortions resulting from propagation through transparent media, is the multiphoton intrapulse interference phase scan (MIIPS). The accuracy of MIIPS, however, is limited when higher-order phase distortions are present. Here we introduce an improvement, called G-MIIPS, which avoids the shortcomings of MIIPS, reduces the influence of higher-order phase terms, and can be used to more efficiently compress broadband laser pulses even with a simple 4f pulse shaper setup. In this work, we present analytical formulas for MIIPS and G-MIIPS, which are valid for chirped Gaussian pulses; we show an approximated analytic expression for G-MIIPS, which is valid for arbitrary pulse shapes. Finally we demonstrate the increased accuracy of G-MIIPS via experiments and numerical simulations.

Fig. 2. Result of single MIIPS iterations, simulated for various phase modulation frequencies while keeping the maximum correction constant Φ0τ2=2.5·104fs2. The figure refers to a Δt=10fs laser pulse after propagation through 10 cm of glass. (a) MIIPS-corrected SHG spectra for different phase-modulation frequencies; the ideal SHG spectrum (black-dashed line) is also shown for reference. (b) Residual phase after MIIPS correction using different phase-modulation frequencies.

Fig. 3. Phase dependence of the SHG intensity at the central frequency of a 100 nm broad laser pulse centered at 800 nm. (a) Map of the SHG in function of the second- and fourth-order phase terms. The dashed line represents the points explored by a typical MIIPS trace. (b) The maximum SHG intensity along the MIIPS trajectory does not correspond to zero GDD.

Fig. 4. Simulation of the compensation of a 10 fs laser pulse centered at 2.4rad/fs after propagation through 10 cm of BK7 glass. Standard MIIPS (a) and G-MIIPS (b) maps, obtained with Φ0=100rad, τ=10fs and σ=0.5rad. The black-dashed lines indicate the GDD range, which can be measured with this set of parameters; the white-dashed line represents both the center of the gate and the points where the GDD is zero. (c) GDD measured by a single iteration of MIIPS (red line) and G-MIIPS (blue line), together with actual GDD value (black line). (d) Residual phase after a single iteration of MIIPS (red line) and G-MIIPS (blue line). (e) SHG signal of the ideal SHG (black line) and after compensation with a single iteration of MIIPS (red line) and G-MIIPS (blue line).

Fig. 5. G-MIIPS for different settings of the gate width, simulated for a 10 fs laser pulse centered at 2.4rad/fs after propagation through 10 cm of BK7 glass. For all cases, the modulation parameters were Φ0=200rad and τ=10fs. Standard MIIPS is also shown for comparison. (a) G-MIIPS map corresponding to σ=1rad. (b) G-MIIPS map corresponding to σ=0.2rad. The black-dashed lines indicate the GDD range, which can be measured with this set of parameters; the white-dashed line represents both the center of the gate and the points where the GDD is zero. (c) SHG after a single iteration of G-MIIPS for σ varying between 1 and 0.2 rad. (d) Residual phase after a single iteration of G-MIIPS for σ varying between 1 and 0.2 rad.

Fig. 6. Simulation of the compensation of a 10 fs laser pulse centered at 2.4rad/fs with significant (105fs4) fourth-order phase distortion. Standard MIIPS (a) and G-MIIPS (b) maps, obtained with Φ0=20rad, τ=10fs, and gate width σ=0.5rad. The black-dashed lines indicate the GDD range, which can be measured with this set of parameters; the white-dashed line represents both the center of the gate and the points where the GDD is zero. (c) GDD measured by a single iteration of MIIPS (red line) and G-MIIPS (blue line), together with actual GDD value (black line). (d) Residual phase after a single iteration of MIIPS (red line) and G-MIIPS (blue line). (e) SHG signal of the ideal SHG (black line) and compensated with a single iteration of MIIPS (red line) and G-MIIPS (blue line). Standard MIIPS in this case reduces SHG.

Fig. 7. Comparison of iterative MIIPS and G-MIIPS. Panels (a) and (c) represent the case of a 10 fs pulse after propagation through 10 cm of glass. Panels (b) and (d) refer to the case of a 10 fs subject to a fourth-order spectral phase of 105fs4. In the panels (a) and (b), it is plotted the residual phase after multiple iterations of either MIIPS (blue dots) or G-MIIPS (green diamonds). In these graphs the first point, labeled with 0, corresponds to the situation before the first iteration. The panels (c) and (d) report the SHG intensity, normalized to its theoretical limit.